Problem: Solve for $x$: $\frac{5x}{(x+3)} - \frac3{(x+3)} = \frac1{(x+3)}$
Answer: First, we combine the fraction on the left to give $\frac{5x-3}{x+3} = \frac{1}{x+3}$.  Then, multiplying both sides by $x+3$ gets rid of the denominators and leaves $5x-3 = 1$.  Adding 3 to both sides gives $5x=4$, so $x = \boxed{\frac{4}{5}}$.